Alert!

Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!

Wednesday, June 6, 2012

Hey hey Ho Ho this aphorism has got to go

I would like to nominate for "teaching aphorism most in need of jettison" right up there with "don't smile until Christmas" :

"Never write anything on the board that is not true"

I heard it first when i was in my masters program (I think) and i heard it most recently today out of a student teacher. It makes me want to hurl. Seriously this strikes me as something some know-nothing said one time that was subsequently repeated by know-littles who want to sound like they know what they are talking about.

I suppose I get why you'd want to adopt this as a guideline when you are super-green and can't manage the most basic of lessons but make no mistake, this is not how learning works.

If you are doing it right your kids will be making conjectures. Conjectures are guesses. Guesses are often wrong. Write them on the board. Be noncommittal as to your agreement with the conjectures. Give the children the air and light to disagree with the conjectures and argue with them. THAT'S MATH. BEING RIGHT ALL THE TIME IS NOT MATH. I CAN'T BELIEVE I HAVE TO SAY THIS.

26 comments:

it's probably a version of the Liar's Paradox ... it got started when someone wrote "Never write anything on the board that is not true" on the board

jokes aside, I probably take too much glee from moments that lead to a student getting to enjoy some furious erasing and brushing of crumbles - especially if I had prefaced the discussion with something like "wait a moment before you try to write all of this down"

it's probably a version of the Liar's Paradox ... it got started when someone wrote "Never write anything on the board that is not true" on the board

jokes aside, I probably take too much glee from moments that lead to a student getting to enjoy some furious erasing and brushing of crumbles - especially if I had prefaced the discussion with something like "wait a moment before you try to write all of this down"

I am trying my best to be similarly non-committal about correct responses as I am about incorrect wild guesses. The idea is - get the kids thinking more about how they would know whether or not their answer makes sense/is correct.

I got my Calculus 2 student evaluations back yesterday. One student seems to believe I have taken your perspective to the extreme, mentioning repeatedly how my starting with the "wrong" way to think about things is bad because whatever he/she sees first sticks.

I love this! Thanks for the validation. Early in the school year, my kids and I were at an impasse; nudging them, then exhorting them to offer their thoughts on a path to a math solution yielded nothing. So reluctant were they to risk being "wrong" that none was willing to offer a suggestion, even a guess. Then, far more out of frustration than epiphany, I wrote a number on the whiteboard (a non-solution).

Finally, a hand shot into the air; "Is that the answer, Mr.C?" Hmmm.

"No, not yet, but it's a starting point," I proffered, "You gotta start somewhere. Now, who's got another idea?" Then, a few more tentative hands went up, more possibilities emerged, but most importantly, the ice had been broken. Following in the liberating wake of a "wrong answer" scrawled on the whiteboard, our discussion flowed more freely. It became okay to hazard a thoughtful guess, even if it wasn't a complete solution.

We have returned to this place time and again. From that point, forward, it became clear to all concerned; writing wrong answers on the whiteboard has given us the freedom to explore intellectual risks without fear of ridicule.

In my first year of teaching I heard a story from my mentor teacher about a former student who had an IEP stating that s/he needed "error free instruction." My immediate reaction was that this was something I could never do. I still feel that way.

If you're asking for student voices--and then only writing some of them on the board--students will quickly learn who are the "smart" ones and will clam up in a hurry.

"I remember interviewing a teacher that said they liked math because with math you can always be right."

And you didn't hire them for this? What? What?!?!?!

THIS IS WHY WE LIKE MATH. AND SCIENCE. AND PHYSICS. WHICH IS LIKE MATH WITH SCIENCE.

Do we really have to argue about this? You KNOW you are a mathy person because the Truth Is Out There. Sure, you might get it wrong on the board the first hundred times, but in the end you know that you can always be right. That there IS a right.

Oh my GOD this attitude is why I want to throw my entire room out of the room. YES we all get that newbies can get all caught up in stupid pedagogical paradigms. But HOLY SHMOKES do we need to find those rare, rare, RARE empiricists and love them and nurture them and hug them and squeeze them and call them George.

I am throwing things now. I hate that you did this. I hate that you are bragging about it in the comments section of a blog that is awesomely about Math being Awesome.

I'm going to go prove something about prime numbers now, which will be RIGHT. Cause I always can, and shlemiels like you can't take that away from me.

Mark C. said, "From that point, forward, it became clear to all concerned; writing wrong answers on the whiteboard has given us the freedom to explore intellectual risks without fear of ridicule." I couldn't agree more. That's the key...setting up an environment in which risk is a welcome pathway to thinking. What's wrong with taking all possible answers under the heading: CONJECTURES, then as they are examined the proven untrue can be crossed off as a visual reminder that the idea was valued but did not work in this case. Like Janettte, I too thank you for sharing your thoughts. I am going to use class surveys because of you. Twitter is crackin me up!Melinda Riccardi

Wow, Jimmy, hulk out much? :) j/k I appreciate your passion. And the angry/funny style. You and Shawn Cornally should get together and go bowling. And I agree with you in a sense - one reason to love math is it tells you things you can be sure are 100% true. On the other hand the most accomplished mathematicians are working on conjectures they suspect are true but don't know for sure yet. The attitude that doing math is a pursuit of repeating procedures, error-free, is destructive to learning, and would be a non-hiring offense if I was interviewing someone too. I hope you'd agree with that so maybe you and James and I are just making different assumptions here on the context of "right all the time."

Not only does the process of developing/discovering new mathematics involve a lot of (educated) guesswork and temporary wrong answers, the results themselves are actually much more relative than people give them credit for.

As an example, "everyone knows" that the angles of a triangle add up to two right angles, just like for the longest time "everyone knew" that the Earth was flat. Neither one turns out to be true.

"...the most accomplished mathematicians are working on conjectures they suspect are true but don't know for sure yet."

THAT hits the nail right on the head, Kate. And it is through that conjectural process that we ferret out (the weasel family returns!) and test those assumptions that ultimately shape the gospel truth (oblique sarcasm intended).

Proffered another way, is the conjectural process not the path along which active learning occurs, and the point of irrefutable rightatude (aka, the "answer"), the destination where *that* journey ends?

Well, I think so... that to learn an idea, being told established truths followed by practice using them to get right answers as quickly as possible is an impoverished and dissatisfying state of affairs. You need to recreate, to the extent possible, that process used when people first discovered those truths (inductive reasoning with examples, conjecture, proof). Pretty sure Piaget thought so too.

I, too, had the ed prof who told us never to write something incorrect on the board for fear that the student would only remember that s/he had seen it on the board in the first place. This strikes me as a deeply cynical point of view that gives the students absolutely no credit for being able to listen as well as see. The value in seeing that the teacher is not connected to some invisible pipeline to the truth is a POWERFUL experience. The students can see that they, too, can master this process not just the sage at the front of the room.

Perhaps my short comment wasn't quite what I intended, which I apologize for, Jimmy. Of course I love math because you can verify results to be correct or not, though not in every branch is that true (say, statistics, where we can only just be more and more certain, and that's also true of science).

But, and this is key, this comment was made by a person that was NOT a mathy person, though wound up as a math teacher through a Fellows program or the like. So they liked that math allowed them to be always right, and we could tell they meant it in the way that they never had to risk being wrong with students. That THEY had the same mindset that we try to get our students out of, to not take risks, to predict, conjecture, estimate. Those three things are just as important to math as proof and correctness, and we weren't seeing it.